53 lines
1.9 KiB
Plaintext
53 lines
1.9 KiB
Plaintext
chapter\<open>Ontologys Mathing\<close>
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theory Ontology_Matching_Example
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imports "Isabelle_DOF.Isa_DOF"
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begin
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text\<open>Using HOL, we can define a mapping between two ontologies.
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It is called ontology matching or ontology alignment.
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Here is an example which show how to map two classes.
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HOL also allows us to map the invariants (ontological rules) of the classes!\<close>
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type_synonym UTF8 = string \<comment> \<open>for the sake of the demonstration\<close>
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definition utf8_to_string
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where "utf8_to_string x = x" \<comment> \<open>for the sake of the demonstration\<close>
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doc_class A =
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first_name :: UTF8
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last_name :: UTF8
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age :: nat
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married_to :: "string option"
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invariant a :: "age \<sigma> < 18 \<longrightarrow> married_to \<sigma> = None"
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doc_class B =
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name :: string
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adult :: bool
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is_married :: bool
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invariant b :: "is_married \<sigma> \<longrightarrow> adult \<sigma>"
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text\<open>We define the mapping between the two classes, i.e. how to transform
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the class @{doc_class A} in to the class @{doc_class B}:\<close>
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definition A_to_B_mapping :: "'a A_scheme \<Rightarrow> B" ("_ \<langle>B\<rangle>\<^sub>A" [1000]999)
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where "\<sigma> \<langle>B\<rangle>\<^sub>A =
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\<lparr> tag_attribute = A.tag_attribute \<sigma>
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, name = utf8_to_string (first_name \<sigma>) @ '' '' @ utf8_to_string (last_name \<sigma>)
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, adult = (age \<sigma> \<ge> 18)
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, is_married = (married_to \<sigma> \<noteq> None) \<rparr>"
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text\<open>Now we check that the invariant is preserved through the morphism:\<close>
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lemma inv_a_preserved :
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"a_inv \<sigma> \<Longrightarrow> b_inv (\<sigma> \<langle>B\<rangle>\<^sub>A)"
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unfolding a_inv_def b_inv_def A_to_B_mapping_def by auto
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lemma A_morphism_B_total :
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"A_to_B_mapping ` ({X::A. a_inv X}) \<subseteq> ({X::B. b_inv X})"
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using inv_a_preserved by auto
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end
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